let x∈[−1,1] andf_n (x)=sin(2narcsinx)
1)prove that f_n is odd and calculate f_n (0) and f_n (1)
2)solve inside [0^ 1] f_n (x)=0
3) prove that f_n is continue,derivable on[−1,1] and
calculate f_n ^′ (x)
4) study the derivability of f_n at 1^− and (−1)^+
5)calculate I_n = ∫_0 ^1 f_n (x)dx .
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